Statics: Lesson 68 - Parallel Axis Theorem, Area Moment of Inertia

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@georgesadler7830 2 жыл бұрын

DR. Hanson, thank you for an excellent presentation of the Parallel Axis Theorem and the Area Moment of Inertia.

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@hmcsee 3 жыл бұрын

Really excellent presentation. I especially appreciate when you explained the significance of moment of inertia so we understand WHAT the number means (higher moment of inertia = higher resistance to bending = stronger shape). Thank you

@carultch 3 жыл бұрын

It really has nothing to do with inertia. It is named "area moment of inertia" because the calculus that defines it is very similar to the calculus that defines moment of inertia in rotational dynamics. The essential difference is that the differential term is area, rather than mass. Second moment of area is a more accurate name. Moment in general means a quantity multiplied by a distance from an origin, added up with that value throughout a system. Second moment means that distance is squared as you calculate it. It comes about because fibers contribute to resistance to bending in two ways, that are both proportional to the distance from the neutral axis. The first way is that the fibers are stressed in proportion to how far they are from the neutral axis, and the second way is that the fibers contribute to resisting the applied bending moment with a "lever arm" that is the distance they are from the neutral axis. When you have a composite assembly of materials that form the beam, Young's modulus also plays a role in each term that gets added up. Beams of a uniform material put Young's modulus as a constant out in front when calculating deflection, because it is term that is the same for all fibers. Composite beams need to include the granularity of how Young's modulus applies to each portion of the beam specifically.

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8:10 "The 2000s...nothing good came out of 😂..."

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@carultch 3 жыл бұрын

Look up R.C. Hibbeler, "Mechanics of Materials"

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@diyaryshwany4244 2 жыл бұрын

I agree 80s music ❤️

@son..2820 Жыл бұрын

for some reason i am now using the Ad's joke to write the parallel axis formula😁😄👍

@angelineromanbautista6295 2 жыл бұрын

static of inertia of composite beams pls? I can learn more if youre the one explaining it. thanks for all the vids

@carultch Жыл бұрын

The idea behind composite beams, is that you use E as a factor to make a weighted average when finding the neutral axis. And rather than only working with the 2nd moment of area as a purely geometric property, you are adding up E*I for every sub-material within the composite. So your centroid is more like a center of elasticity and area, than purely a center of area. And your 2nd moment of area, is more like a 2nd moment of elasticity and area.